Global existence of weak solutions to the Fried–Gurtin model of phase transitions

Volume 34 / 2007

Zenon Kosowski Applicationes Mathematicae 34 (2007), 413-430 MSC: 35D05, 35K60, 35Q72, 74B20. DOI: 10.4064/am34-4-5

Abstract

We prove the existence of global in time weak solutions to a three-dimensional system of equations arising in a simple version of the Fried–Gurtin model for the isothermal phase transition in solids. In this model the phase is characterized by an order parameter. The problem considered here has the form of a coupled system of three-dimensional elasticity and parabolic equations. The system is studied with the help of the Faedo–Galerkin method using energy estimates.

Authors

  • Zenon KosowskiInstitute of Mathematics and Cryptology
    Faculty of Cybernetics
    Military University of Technology
    S. Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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